Statistical Methods for Degradation Data With Dynamic Covariates Information and an Application to Outdoor Weathering Data

Yili Hong,Yuanyuan Duan,William Q Meeker,Deborah L Stanley,Xiaohong Gu

doi:10.1080/00401706.2014.915891

Abstract

Degradation data provide a useful resource for obtaining reliability information for some highly reliable products and systems. In addition to product/system degradation measurements, it is common nowadays to dynamically record product/system usage as well as other life-affecting environmental variables, such as load, amount of use, temperature, and humidity. We refer to these variables as dynamic covariate information. In this article, we introduce a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with individual random effects to describe degradation paths and a vector time series model to describe the covariate process. Shape-restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters in the degradation data model and the covariate process model are estimated by using maximum likelihood. We also describe algorithms for computing an estimate of the lifetime distribution induced by the proposed degradation path model. The proposed methods are illustrated with an application for predicting the life of an organic coating in a complicated dynamic environment (i.e., changing UV spectrum and intensity, temperature, and humidity). This article has supplementary material online.

Highlights

1.1 MotivationFor products and systems with high reliability, it is challenging to do field reliability assessment in a timely manner based only on limited lifetime data
For products with degradation driven by usage and environmental conditions, information about these variables can be important for modeling the degradation process
Based on the simulation results, we find that the relative root MSE (RMSE) of the point estimators of the parameters and the UV effect function generally decrease as n and m increase

Summary

Introduction

1.1 MotivationFor products and systems with high reliability, it is challenging to do field reliability assessment in a timely manner based only on limited lifetime data. For products with degradation driven by usage and environmental conditions, information about these variables can be important for modeling the degradation process. It is common nowadays to dynamically record product/system usage and load as well as other environmental variables such as temperature and humidity, which we refer to as dynamic covariate information. Even a small device like a power inverter that is used in solar panel arrays can gather and transmit information on the output of power, the ambient temperature, and humidity every few seconds. The availability of such large-scale dynamic data creates many opportunities and challenges

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